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Homotopy theory of the suspensions of the projective plane
 Memoirs AMS
"... Abstract. The homotopy theory of the suspensions of the real projective plane is largely investigated. The homotopy groups are computed up to certain range. The decompositions of the self smashes and the loop spaces are studied with some applications to the Stiefel manifolds. ..."
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Cited by 12 (8 self)
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Abstract. The homotopy theory of the suspensions of the real projective plane is largely investigated. The homotopy groups are computed up to certain range. The decompositions of the self smashes and the loop spaces are studied with some applications to the Stiefel manifolds.
EHP spectra and periodicity. I. Geometric constructions
 Trans. Amer. Math. Soc
, 1993
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Cited by 8 (1 self)
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JSTOR is a notforprofit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.
Printed in Great Britain 73 Generalized splitting theorems
, 1982
"... In (5), we and Fred Cohen gave some quite general splitting theorems. These described how to decompose the suspension spectra of certain filtered spaces CX as wedges of the suspension spectra of their successive filtration quotients Dq X. The spaces CX were of the form Cr xIr/ ( ~) for suitable sequ ..."
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In (5), we and Fred Cohen gave some quite general splitting theorems. These described how to decompose the suspension spectra of certain filtered spaces CX as wedges of the suspension spectra of their successive filtration quotients Dq X. The spaces CX were of the form Cr xIr/ ( ~) for suitable sequences of spaces {Cf} and {Xr}, and the construction CX was intended to be a reworking in 'proper generality ' of the constructions introduced in (9). We no longer believe that sufficient generality was achieved in (5). The original motivation concerned iterated loop spaces Q. n T, n X, where X is path connected. Consider a cofibration i: A>X, where A is also connected. Let 8: X/A^C(i)>'LA be the standard map and consider the fibre Fn(X, A) of Q n 1 S m ~ 1 (3) (n> 1). By a slight elaboration of the argument in (9), §6, which gives complete details when X is the cone on A, there is a commutative diagram En (X. A) Fn (X, A) where the bottom row is the canonical fibration. By (9), 73, the top row is a quasifibration.
BRAYTON GRAY
"... arXiv version: fonts, pagination and layout may vary from GTM published version Filtering the fiber of the pinch map ..."
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arXiv version: fonts, pagination and layout may vary from GTM published version Filtering the fiber of the pinch map
DECOMPOSITIONS INVOLVING ANICK’S SPACES
, 804
"... The goal of this work is to continue the investigation of the Anick fibration and the associated spaces. Recall that this is a plocal fibration sequence: Ω 2 S 2n+1 πn 2n−1 2n+1 − → S − → T − → ΩS where πn is a compression of the p r th power map on Ω 2 S 2n+1. This fibration was first described fo ..."
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The goal of this work is to continue the investigation of the Anick fibration and the associated spaces. Recall that this is a plocal fibration sequence: Ω 2 S 2n+1 πn 2n−1 2n+1 − → S − → T − → ΩS where πn is a compression of the p r th power map on Ω 2 S 2n+1. This fibration was first described for p � 5 as the culmination of a 270 page book [A]. In [AG], the authors described an H space structure for the fibration sequence. Its relationship to EHP spectra was discussed [G3] as well as first steps to developing a universal property. Much work has been done since then to find a simpler construction, and this was obtained for p � 3 in [GT]. This new construction also reproduces the results of [AG]. It is in the context of these new methods that this work is developed and we assume a familiarity with [GT]. One of the main features of the construction is a certain fibration sequence: ΩG h − → T i − → R ρ − → G where h has a right homotopy inverse g: T → ΩG and the adjoint of g: ˜g: ΣT → G also has a right homotopy inverse f: G → ΣT. Together these maps define an H space structure on T and a coH space structure on G, and both G and T are atomic. Furthermore R ∈ W ∞ r, the class of spaces that are the one point union of mod ps Moore spaces for r � s. For some applications it would be helpful to have a better understanding of the map ρ. In order to accomplish this, we reconstruct a space D from [A]. D is closely related to G. Although the formal properties of D are not as simple as G (it is not a coH space) other properties are simpler (for example Theorem A part (b) below). Define C = P 2npi +1 ( p r+i−1). i=1 Theorem A. There is a cofibration sequence: C c − → G → D 1 2 BRAYTON GRAY and a fibration sequence: